[tex]\frac{\overline{xy5xy}}{\overline{xy}+5}[/tex]
[tex]\overline{xy5xy}=10000x+1000y+500+10x+y=10010x+1001y+500=1001(10x+y)+500[/tex]
[tex]\overline{xy}=10x+y[/tex]
Notam 10x+y=a
Vom avea:
[tex]\frac{1001a+500}{a+5}[/tex] ∈N
[tex]\frac{1001a+500}{a+5}=\frac{1001(a+5)-4505}{a+5} =1001-\frac{4505}{a+5}[/tex]
a+5 | 4505
a+5={17,53,85}- doar cele de 2 cifre
a={12,48,80}
[tex]10x+y=\overline{xy}=\{12,48,80\}[/tex]
Suma valorilor=12+48+80=140
